From Guild Wars Wiki
Dedication is a permanent status that
miniatures receive when stored in the
Hall of Monuments. It is similar to
customization in that it can be done only once and is player specific, but instead of completely preventing use by other players, it merely prevents that miniature from being stored in other players' Halls.
- Before Dedication was implemented, the Hall of Monuments allowed players to customize miniatures instead. If you take a customized miniature back to the Hall of Monuments, it will give you the option to remove the customization and dedicate the miniature instead.
